The subject matter of this invention relates generally to strain estimating apparatus and more particularly to apparatus for ascertaining when an inaccessible portion of a turbine generator system shaft will break.
It has been observed in connection with electrical turbine generator systems that the capability exists for mechanical torsional oscillations to be produced along portions of the shaft of the mechanical system which could cause shaft damage or fracture. Torsional monitoring systems have been provided to maintain a record of the disturbances that occur on machines due to transmission system faults such as short circuits, transmission system switching, out-of-phase synchronizing accidents and transient disturbances in series capacitor compensating electrical systems which are interconnected with the turbine generator system. With each of these types of disturbances the generator is subject to a high amplitude torsional shock together with transient oscillatory torque components. The frequency of the torque oscillations depends upon the type of transient and the components of the electrical system. The decay rate of these oscillations is primarily determined by the characteristic of the electrical system, but it can be influenced by the interaction of the torsional mechanical system of the turbine generator rotor. Initial torque amplitudes are dependent upon the type of disturbance, the configuration of the transmission system, and the location of the disturbance. It has been observed that disturbances of the type previously described frequently excite torsional natural frequencies of the rotor systems. Such excitation can cause torsional stresses at critical locations along the shaft which exceed the fatigue endurance limits of the shaft materials. Once the limit is exceeded theoretical analyses and sample tests have demonstrated that fatigue life is expended. The effects of repeated disturbances of the types described are cumulative and can, over a period of time, lead to a failure in the form of fatigue cracks appearing in the shafts. It is therefore desirous to provide torsional oscillation monitoring systems for the rotating mechanical system. The addition of a torsional monitoring system will provide a cumulative record of fatigue life expended, to provide information on the relative severity of different types of shock so that system operators can modify unsafe practices, and to provide information to show which portions of the shaft system should be carefully inspected during maintenance periods or following particularly severe disturbances. It has been observed that when this phenomenon occurs the rotating masses on the common turbine-generator shaft torsionally oscillate one with respect to the other, to the extent that interconnecting portions of the shaft are exposed to significant strain. As the strain increases, a limit in the metallurgical properties of the shaft is reached at which the shaft breaks. For obvious reasons, the fracture of a shaft rotating at speeds approximately thirty-six hundred revolutions per minute is very undesirous. The aforementioned has interested the designers, manufacturers, and producers of rotating electrical equipment of this kind since the first shaft break was discovered. Significant efforts have been put forth to attempt to solve the problem of the undesired shaft breakage or other damage. A solution for the aforementioned problem is constant direct monitoring of the strain on the shaft. Theoretically, the idea is workable, unfortunately though problems exist which usually prevents the implementation of the theory in a convenient and easy manner. Specifically, most portions of the shaft are so situated relative to the rotating masses and the protective shrouds, shields, and the like associated therewith that direct monitoring is difficult or impossible. In the past, therefore, apparatus was developed for indirect monitoring of shaft characteristics for detecting when that level of shaft strain is approached where shutdown and replacement or similar corrective action is necessary. For purposes of simplicity, the aforementioned approach is sometimes referred to as the "lumped parameter approach". An example of this approach can be found in U.S. Pat. No. 4,051,427, issued Sept. 27, 1977 to L. A. Kilgore et al. and assigned to the assignee of the present invention. In this case, a parallel analog computer model which represents all or most of the elements of the rotating shaft is provided for utilization with detectable electromechanical variables such as local shaft torque and local shaft speed. This model provides a real time side-by-side representation of the actual mechanical system. It is coordinated at its inputs with measurable variables from the actual system so that it reacts in response thereto. In order to construct the analog model, various mechanical system parameters such as mass, shaft resilience, and damping are determined and utilized. For example, shaft resilience and shaft damping can be represented for that portion of the shaft between two arbitrarily chosen rotating masses. In the model thus produced, electrical sampling of those model regions which corresponds to inexcessible regions in the turbine generator can be made to detect what oscillatory characteristics exist in the actual mechanical system. Records of strain, peak velocities and the like can be thus obtained, stored and otherwise utilized in some meaningful fashion to help provide useful, safe, non-destructive operation for the actual turbine generator. A system of this type is useful. However, as implemented in the prior art it has some disadvantages. One disadvantage lies in the fact tht a one-to-one correspondence between the actual shaft parameters and the model parameters is required. This means that for every mass on the shaft there should be a portion of the model directly related to that mass and so on for resilience, damping etc. This means that there must be at least as many elements in the model as there are in the shaft. For relatively complex electro-mechanical systems, the number of model units is proportional to the number of units in the large electro-mechanical system. This tends to increase the relative size and complexity of the model thus introducing all the problems associated with relatively complex systems including inaccuracies due to component variances, model stability, cost, etc. Furthermore, the relationship between the model and the actual system is such that it is not easy to decouple the effects of the various parameters one from the other. This means it is very difficult to determine which of the parameters in the actual system most contributes to the problem being detected in the model system. That is not to say that a problem cannot be detected if one arises, but merely to say that the cause of the problem cannot be easily isolated. It would seem that the next logical step for solving the kinds of problems previously described would be to separate the most significant parameters associated with the torsional oscillation problems for the purposes of providing monitoring systems that can be adjusted or modified without rebuilding or restructuring the electrical model. Observers of the torsional oscillation problem have sensed that one of the most significant contributing factors to the problem is a frequency phenomena. However, the lumped parameter system makes no provision for adjusting critical frequencies. Consequently, it would be advantageous if a monitoring and detecting system could be provided which was relatively accurate, inexpensive, and had a minimum of components. Furthermore, it would be desirous if this system somehow could be utilized to pinpoint or focus on portions of the electromechanical system which contribute most to the torsional oscillation problem. It would be even further advantageous if the concept of frequency could somehow be explicitly introduced into the output of the model so that certain less critical frequency values could somehow be eliminated without seriously affecting the solution. In the past, a model analysis technique has been utilized to attempt to introduce a frequency related concept into analysis of machine characteristics. This can be found in a paper entitled, "Mechanische Beanspruchung von Tubosaetzen Bli Elektrischen Stoerungen and Ploezlichen Lastaenderingen" by D. Lanabrecht and K. Large. The paper was presented at an ETG technical meeting on power plant generators, Mannheim, Germany, Nov. 8, 1977 (English translation in KWU Publication 442-101). Furthermore, the torsional stress analyzer which uses techniques related to those described in the aforementioned paper is taught in U.S. Pat. No. 4,057,714, entitled, "Durability or Service-Life Monitoring Device for Turbogenerator Shaft" by K. Fork et al., issued Nov. 8, 1977 on a German foreign priority date of Sept. 30, 1975. The modal analysis technique is utilized to represent a given number of rotating masses on a common shaft at a given frequency of rotation by a number of separate effective masses each vibrating at its own modal frequency and its own modal amplitude. This has the effect of introducing a frequency component into the input of the torsional analysis concept. However, in the teaching of the previous patent and paper, monitoring of data for each rotating mass in the actual system is required. Of course, this does not solve the problem of the inaccessibility of certain rotating masses. In other instances, a substitution of actual information about each rotating mass with secondary information (i.e. precalculated torque) related to each individual rotating mass is required. But, this of course has the same drawback as the "lumped parameter" model described previously. Furthermore, the required turbine moments are determined from steam pressures and valve positions for various high pressure, intermediate pressure and low pressure steam turbine stages. This increases the complication of the monitoring system and consequently the cost. Even though modal analysis is utilized for preliminary analysis in the later case, it does not appear to be utilized as an output in the electronic shaft torsional model. In a paper from the IEEE Transactions on Power Apparatus and Systems, Vol. PAS-97, No. 5, September/October 1978, entitled "The Navajo SMF Type Subsynchronous Resonance Relay", modal filters are used to provide a signal for relaying purposes. But, the signals are not recombined after passing through the modal filters so there can be no calculation of instantaneous shaft torque or stress with that system. This system is useful in providing information about individual modal frequencies, but because of the phase shifting effect of each filter it is not useful for generally instantaneously providing a complete picture of the modal response of the entire mechanical system. It would therefore be advantageous to find a system which utilized the modal analysis techniques in conjunction with an electronic shaft torsional model where a minimum number of inputs were required for accurate analysis to avoid the problem of the inaccessibility of certain portions of the turbine generator system for monitoring. It would be further advantageous if frequency related decoupling could be utilized in the model so that a determination of shaft strain and thus torsional fatigue could be related to the various frequencies of the torsional model. It would be even further advantageous if the component modal analysis data for certain frequencies could be instantaneously combined for a better representation of the effect of torsional oscillation.